Question

State whether the following statement is true or false:

If a < b, then ac > bc.

Answer 1

This statement is false.

Given,

a < b

If c is a positive number,

Multiplying both sides by c we get,

ac < bc

If c is a negative number,

Multiplying both sides by c we get,

ac > bc [Using rule 4]

Hence, the statement is false.